Line Integrals or Contour Integrals:
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Line Integrals or Contour Integrals: Suppose that $z \equiv z(t)$ for $t \in [a, \; b]$ represent a contour (that is, piecewise smooth curve) $C$, extending from a point $z_{1} = z(a)$ to a point $z_{2} = z(b)$. Let the function $f(z)$ be defined on $C$. We define the line integral or contour integral of $f$ along the curve $C$ as follows:

MATH

Example: Compute MATH where $C$ is given by $z(t) = 2e^{it}$ for MATH.
Observe that MATH for MATH. Therefore,

MATH

 
 
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